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		<h1 id="0059-cairo-iii--circles-and-arcs">0059: Cairo III – Circles and Arcs</h1>

<p>Let’s jump right in and look at…</p>

<h2 id="drawing-a-circle">Drawing a Circle</h2>

<div class="screenshot-frame">
	<div class="frame-header">
		Results of this example:
	</div>
	<div class="frame-screenshot">
		<figure>
			<img id="img0" src="../images/screenshots/018_cairo/cairo_09.png" alt="Current example output" />		<!-- img# -->
			
			<!-- Modal for screenshot -->
			<div id="modal0" class="modal">																	<!-- modal# -->
				<span class="close0">&times;</span>															<!-- close# -->
				<img class="modal-content" id="img00" />															<!-- img## -->
				<div id="caption"></div>
			</div>
			
			<script>
			// Get the modal
			var modal = document.getElementById("modal0");														// modal#
			
			// Get the image and insert it inside the modal - use its "alt" text as a caption
			var img = document.getElementById("img0");															// img#
			var modalImg = document.getElementById("img00");													// img##
			var captionText = document.getElementById("caption");

			img.onclick = function()
			{
			  modal.style.display = "block";
			  modalImg.src = this.src;
			  captionText.innerHTML = this.alt;
			}
			
			// Get the <span> element that closes the modal
			var span = document.getElementsByClassName("close0")[0];											// close#
			
			// When the user clicks on <span> (x), close the modal
			span.onclick = function()
			{ 
				modal.style.display = "none";
			}
			</script>
			<figcaption>
			Current example output
			</figcaption>
		</figure>
	</div>

	<div class="frame-terminal">
		<figure class="right">
			<img id="img1" src="../images/screenshots/018_cairo/cairo_09_term.png" alt="Current example terminal output" />		<!-- img#, filename -->

			<!-- Modal for terminal shot -->
			<div id="modal1" class="modal">																				<!-- modal# -->
				<span class="close1">&times;</span>																		<!-- close# -->
				<img class="modal-content" id="img11" />																		<!-- img## -->
				<div id="caption"></div>
			</div>
			
			<script>
			// Get the modal
			var modal = document.getElementById("modal1");																	// modal#
			
			// Get the image and insert it inside the modal - use its "alt" text as a caption
			var img = document.getElementById("img1");																		// img#
			var modalImg = document.getElementById("img11");																// img##
			var captionText = document.getElementById("caption");

			img.onclick = function()
			{
			  modal.style.display = "block";
			  modalImg.src = this.src;
			  captionText.innerHTML = this.alt;
			}
			
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			var span = document.getElementsByClassName("close1")[0];														// close#
			
			// When the user clicks on <span> (x), close the modal
			span.onclick = function()
			{ 
				modal.style.display = "none";
			}
			</script>

			<figcaption>
				Current example terminal output (click for enlarged view)
			</figcaption>
		</figure>
	</div>

	<div class="frame-footer">																								<!-- ------------- filename (below) --------- -->
		The code file for this example is available <a href="https://github.com/rontarrant/gtkd_demos/blob/master/018_cairo/cairo_09_draw_circle.d" target="_blank">here</a>.
	</div>
</div>

<p>The essence of circle drawing is this:</p>

<div class="language-d highlighter-rouge"><div class="highlight"><pre class="highlight"><code><span class="kt">bool</span> <span class="n">onDraw</span><span class="p">(</span><span class="n">Scoped</span><span class="p">!</span><span class="n">Context</span> <span class="n">context</span><span class="p">,</span> <span class="n">Widget</span> <span class="n">w</span><span class="p">)</span>
<span class="p">{</span>
	<span class="n">context</span><span class="p">.</span><span class="n">setLineWidth</span><span class="p">(</span><span class="mi">3</span><span class="p">);</span>
	<span class="n">context</span><span class="p">.</span><span class="n">arc</span><span class="p">(</span><span class="mi">330</span><span class="p">,</span> <span class="mi">160</span><span class="p">,</span> <span class="mi">40</span><span class="p">,</span> <span class="mi">0</span><span class="p">,</span> <span class="mi">2</span> <span class="p">*</span> <span class="mf">3.1415</span><span class="p">);</span>
	<span class="n">context</span><span class="p">.</span><span class="n">stroke</span><span class="p">();</span>
		
	<span class="k">return</span><span class="p">(</span><span class="kc">true</span><span class="p">);</span>
		
<span class="p">}</span> <span class="c1">// onDraw()</span>
</code></pre></div></div>

<p>And even though you might expect a <code class="language-plaintext highlighter-rouge">circle()</code> function, we actually use <code class="language-plaintext highlighter-rouge">arc()</code>… and since an arc is just an incomplete circle, well… there you go.</p>

<p>The arguments to the <code class="language-plaintext highlighter-rouge">arc()</code> function are:</p>

<ul>
  <li>x position of the circle’s center,</li>
  <li>y position of the circle’s center,</li>
  <li>the circle radius (as if the circle were complete),</li>
  <li>the point along the arc where we start drawing, and</li>
  <li>the point along the arc where we stop drawing.</li>
</ul>

<p>Those last two arguments are in radians. That’s why the point where we stop drawing is two times PI.</p>

<h3 id="the-wikipediacairo-anomaly">The <em>Wikipedia</em>/<em>Cairo</em> Anomaly</h3>

<p>When I first started exploring the <code class="language-plaintext highlighter-rouge">arc()</code> function, I wasn’t getting the results I expected. My confusion was twofold:</p>

<ul>
  <li>I had assumed that 0 degrees (and therefore 0.0 radians) was true north like it is on a compass, and</li>
  <li>I also assumed that, like a compass, degrees increase in a clockwise direction around the circle.</li>
</ul>

<p>So, I <em>Google</em>d radians and read the <em>Wikipedia</em> page. However, their conversion chart showed 0 to the east, compass-wise, and both degrees and radians increasing counterclockwise.</p>

<p>Eventually, I realized that <em>Cairo</em> agreed with <em>Wikipedia</em> on one count, but not the other.</p>

<p>So, here’s the straight dope on radians according to <em>Cairo</em>:</p>

<ul>
  <li>0 is to the east (compass east), and</li>
  <li>radians increase in value in a clockwise direction.</li>
</ul>

<p>Not being much of a mathematician, I have no idea why 0 faces east and I certainly don’t know why <em>Wikipedia</em>’s conversion chart has radians increasing in a counter-clockwise direction. But <em>Cairo</em> agrees with real-world clocks and compasses, so at least we have those as jumping off points for understanding what’s going on with <em>Cairo</em> arcs.</p>

<p>So I took the liberty of reproducing the conversion chart so it accurately reflects <em>Cairo</em>’s worldview:</p>

<div class="inpage-frame">
	<figure class="center">
		<img src="../images/diagrams/018_cairo/degrees_radians_clockwise.png" alt="Figure 1: Degrees and Radians, Clockwise" style="width: 600px; height: 600px;" class="center" />
		<figcaption>
			Figure 1: Degrees/radians conversion in the Cairo worldview. 
		</figcaption>
	</figure>
</div>

<h2 id="drawing-an-arc">Drawing an Arc</h2>

<div class="screenshot-frame">
	<div class="frame-header">
		Results of this example:
	</div>
	<div class="frame-screenshot">
		<figure>
			<img id="img2" src="../images/screenshots/018_cairo/cairo_10.png" alt="Current example output" />		<!-- img# -->
			
			<!-- Modal for screenshot -->
			<div id="modal2" class="modal">																<!-- modal# -->
				<span class="close2">&times;</span>														<!-- close# -->
				<img class="modal-content" id="img22" />														<!-- img## -->
				<div id="caption"></div>
			</div>
			
			<script>
			// Get the modal
			var modal = document.getElementById("modal2");													// modal#
			
			// Get the image and insert it inside the modal - use its "alt" text as a caption
			var img = document.getElementById("img2");														// img#
			var modalImg = document.getElementById("img22");												// img##
			var captionText = document.getElementById("caption");

			img.onclick = function()
			{
			  modal.style.display = "block";
			  modalImg.src = this.src;
			  captionText.innerHTML = this.alt;
			}
			
			// Get the <span> element that closes the modal
			var span = document.getElementsByClassName("close2")[0];										// close#
			
			// When the user clicks on <span> (x), close the modal
			span.onclick = function()
			{ 
				modal.style.display = "none";
			}
			</script>
			<figcaption>
			Current example output
			</figcaption>
		</figure>
	</div>

	<div class="frame-terminal">
		<figure class="right">
			<img id="img3" src="../images/screenshots/018_cairo/cairo_10_term.png" alt="Current example terminal output" /> 		<!-- img#, filename -->

			<!-- Modal for terminal shot -->
			<div id="modal3" class="modal">																			<!-- modal# -->
				<span class="close3">&times;</span>																	<!-- close# -->
				<img class="modal-content" id="img33" />																	<!-- img## -->
				<div id="caption"></div>
			</div>
			
			<script>
			// Get the modal
			var modal = document.getElementById("modal3");																// modal#
			
			// Get the image and insert it inside the modal - use its "alt" text as a caption
			var img = document.getElementById("img3");																	// img#
			var modalImg = document.getElementById("img33");															// img##
			var captionText = document.getElementById("caption");

			img.onclick = function()
			{
			  modal.style.display = "block";
			  modalImg.src = this.src;
			  captionText.innerHTML = this.alt;
			}
			
			// Get the <span> element that closes the modal
			var span = document.getElementsByClassName("close3")[0];													// close#
			
			// When the user clicks on <span> (x), close the modal
			span.onclick = function()
			{ 
				modal.style.display = "none";
			}
			</script>

			<figcaption>
				Current example terminal output (click for enlarged view)
			</figcaption>
		</figure>
	</div>

	<div class="frame-footer">																							<!--------- filename (below) ------------>
		The code file for this example is available <a href="https://github.com/rontarrant/gtkd_demos/blob/master/018_cairo/cairo_10_draw_arc.d" target="_blank">here</a>.
	</div>
</div>

<p>You may be ahead of me on this one, but drawing an arc is the same as drawing a circle except that the start and end points stop short of describing the entire circle:</p>

<div class="language-d highlighter-rouge"><div class="highlight"><pre class="highlight"><code><span class="kt">bool</span> <span class="n">onDraw</span><span class="p">(</span><span class="n">Scoped</span><span class="p">!</span><span class="n">Context</span> <span class="n">context</span><span class="p">,</span> <span class="n">Widget</span> <span class="n">w</span><span class="p">)</span>
<span class="p">{</span>
	<span class="kt">float</span> <span class="n">x</span> <span class="p">=</span> <span class="mi">320</span><span class="p">,</span> <span class="n">y</span> <span class="p">=</span> <span class="mi">180</span><span class="p">;</span>
	<span class="kt">float</span> <span class="n">radius</span> <span class="p">=</span> <span class="mi">40</span><span class="p">,</span> <span class="n">startAngle</span> <span class="p">=</span> <span class="mf">0.7</span><span class="p">,</span> <span class="n">endAngle</span> <span class="p">=</span> <span class="mf">2.44</span><span class="p">;</span>

 	<span class="c1">// draw the arc</span>
	<span class="n">context</span><span class="p">.</span><span class="n">setLineWidth</span><span class="p">(</span><span class="mi">3</span><span class="p">);</span>
	<span class="n">context</span><span class="p">.</span><span class="n">arc</span><span class="p">(</span><span class="n">x</span><span class="p">,</span> <span class="n">y</span><span class="p">,</span> <span class="n">radius</span><span class="p">,</span> <span class="n">startAngle</span><span class="p">,</span> <span class="n">endAngle</span><span class="p">);</span>
	<span class="n">context</span><span class="p">.</span><span class="n">stroke</span><span class="p">();</span>

	<span class="k">return</span><span class="p">(</span><span class="kc">true</span><span class="p">);</span>
		
<span class="p">}</span> <span class="c1">// onDraw()</span>
</code></pre></div></div>

<p>If you consult the conversion chart, you’ll see that the arc starts at about 40 degrees (south-southeast in <em>Cairo</em>’s version of the universe) and goes to 140 degrees. And remember, drawing is done in a clockwise direction, so even though the start point is to the right of the end point (effectively, right to left) it’s still a clockwise <code class="language-plaintext highlighter-rouge">stroke()</code>.</p>

<h2 id="conclusion">Conclusion</h2>

<p>Next time, we’ll continue on and cover fills, then double back and have a bit of fun with arcs.</p>

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